We tested our methods on two previously published metagenomic datasets, which were downloaded from the NCBI Trace Archive or Short Read Archive databases: (1) gut microbiomes from obese and lean twins 3; (2) metagenomes from adult- and infant-type gut microbiomes 7. Each dataset is divided into two populations of distinct phenotypes. The metabolic pathway data were downloaded from the KEGG pathways database 6. The metabolic network is represented as a graph where nodes are metabolic substrates, and edges are molecular reactions (Fig. 1). The edges could be unidirectional or bidirectional depending on whether the corresponding reaction is reversible (as specified in KEGG database). Multiple reactions that are related to a same biological process are aggregated by KEGG into a “pathway” (e.g., glycolysis pathway). In addition, we refer to the network comprising all metabolic pathways in KEGG as the “global metabolic network”. Metagenomic sequences are annotated through BLASTX searches against KEGG genes database. The abundance of each molecular reaction is estimated as the number of metagenomic sequences mapped to it. Note that more accurate abundance estimates can be obtained by taking into account the length of individual genes 12 and we plan to explore the use of such estimates (and the associated statistics) in future versions of our software.

To score the biological activity of a particular subnetwork, we first use Metastats 9 to calculate the significance of differential abundance for each reaction between the two phenotypic groups under comparison. Under the null hypothesis, the relative abundances are randomly drawn from the same distribution across different phenotypic groups, thus the p value for each feature (metabolic reactions) follows a uniform distribution from 0 to 1. Based on this assumption, p values can be converted to Z scores 13 using the Gaussian distribution. Because Metastats performs a two-tailed test for each reaction, the two-tailed p values can be converted back to the original Z values using the following equation:

where is the inverse cumulative density function (CDF) of standard normal distribution; G1 and G2 represent two different phenotypic groups. Using this formula, if a reaction is more abundant in population G1, then its Z score will be positive and vice versa. We are specifically interested in finding a pathway whose reactions are either enriched or depleted as a whole, as apposed to previous approaches 1314 that identify active or perturbed subnetworks, which may contain a mixture of enriched and depleted components. Similar to the approach of 13 we define the aggregate score for a particular subnetwork to be the sum of the Z scores over all reactions contained within it: , where k is the size (number of metabolic reactions) of the subnetwork.

As proposed in 13, we attempt to find subnetworks that maximize the cumulative Z- score defined above. Unfortunately, this problem is NP-hard, which is equivalent to finding a maximum-weight subgraph 13. Several approaches to solving this problem have been previously proposed: Ideker, et al. 2002 13 used simulated annealing, but this heuristic is slow; Dittrich, et al, 2008 14 used integer linear programming that can find provably optimal subpathways quickly, but it requires the commercial software package CPLEX that is not available to the general public (using a freely available ILP solver would require re-implementing the entire algorithm as the software is provided as a binary-only release). Here we rely on a greedy search heuristic that is fast, and, while not guaranteed to find maximally scoring pathways, performs well in practice. The algorithm we employ is described below:

This algorithm tries to find a connected metabolic subnetwork, which can have any arbitrary structure, with maximum weight. However, it is believed that in metabolic networks, chains are especially more biologically meaningful and interesting, because they attempt to capture the structure of a series of reactions that are successively connected. To allow this idea, we modify line 8 of the above algorithm to “Pick an edge e_j which has the highest weight of the edges that are adjacent to and have the same direction with e_j-1”. Both searching algorithms are implemented in our program and can be selected through command-line parameters. To find all significant subnetworks (computing significance is discussed below), we iteratively remove the edges in the global network that are contained in previously found significant subnetworks, and rerun our greedy search on the rest of the network until we can no longer find any additional significant subnetworks. Note, that unlike the original version of our code 15, the search algorithm is not limited to given subnetwork size, rather will find all significant subnetworks irrespective of size.

The null score distribution for a specific subnetwork can be estimated by permuting the sample labels (columns of the abundance matrix) of the reactions and computing the subnetwork scores from the permuted abundance matrix. The significance p value is estimated as the number of random permutations that produce higher scores than the original subnetwork. The p value computed through this approach (termed p_abund throughout the rest of the paper), however, ignores the topology of the underlying global metabolic network, and potentially leads to incorrect conclusions. For example, assume we have a densely connected metabolic network, in which every edge is connected with all other edges. Then, the best subnetwork is simply composed of the top differentially abundant metabolic reactions. This indicates that whenever there are significant reactions, which may simply come from random noise given the large number of edges, they will form a significant subnetwork because of the biases from the network topology (Fig. 2). To address this problem, we compute another p value (termed p_struct), relying on a topological definition of the null distribution of subnetwork scores. Specifically, instead of treating each subnetwork as a bag of genes, we estimate the distribution of scores for actual subnetworks identified within the underlying global metabolic network. Since this null-distribution depends on the size (number of edges) of the subnetwork, let k be the size of a subnetwork generated by the greedy search algorithm described above, and Z be the corresponding Z-score. The p_struct value for this subnetwork can be calculated as follows: (i) permute the edge weights (row labels of the abundance matrix) of the global metabolic network; (ii) perform greedy search to find a maximal weighted subnetwork of size k; (iii) repeat step 1 and step 2 for 1000 times, and generate 1000 weights of the max-weight subnetwork (null distribution); (iv) the p_struct value is the proportion of the 1000 times in step 3 that we see scores higher than our original observation Z.

To summarize the methods described above, the MetaPath algorithm proceeds as follows:

1. Differential abundance is assessed on an edge-by-edge basis (reaction-by-reaction) using Metastats;

2. The significance estimates (p-values) from Metastats are fed into a greedy search algorithm to determine all maximally weighted subnetworks(in terms of statistical Z-scores) in the global metabolic network;

3. The significance of each subnetwork detected by the greedy search algorithm is assessed using both a topology-independent bootstrapping approach (p_abund), and a topology-dependent bootstrapping approach (p_struct);

4. The subnetworks determined to be significant (p_abund ≤ 0.05 and p_struct ≤ 0.05) are reported to the user (Note: the threshold for significance can be adjusted through command-line parameters). The pathways are ranked by p_abund values.

In order to validate our methods, we have designed a simulated metagenomic study and compared the results with three previous approaches: (i) identifying significantly active subnetworks using simulated annealing and greedy search 13; (ii) discovering significant individual reactions using Metastats 9; and (iii) finding differentially abundant KEGG defined pathways, an approach widely used in metagenomic functional comparison 3710. We choose these tools because they are addressing similar biological problems. However they do not solve the exact same problem as this paper, which is finding differentially abundant subnetworks that may span two or more KEGG defined pathways (see discussion in the Background section). Here the goal of this simulated study is to show that the computational problem in this paper can not be directly solved by applying methods previously developed in a related context.

We designed a simulated metabolic pathways dataset in which five subjects are created for each of the two groups with distinct phenotypes. To generate the artificial reaction abundance matrix (where rows represent reactions and columns represent subjects), a Gaussian distribution is created for each reaction, whose mean is randomly chosen from a real metagenomic dataset (gut microbiome from obese and lean subjects 3). The variance of each distribution is calculated by setting the relative standard deviation (standard deviation divided by the mean) to 0.2. If we define a reaction to be equally abundant between two groups under comparison, then a random abundance value is generated from the same distribution for each subject. Otherwise, if a reaction is defined to be significantly enriched in one group, then another normal distribution is created for this reaction by increasing the mean such that the p value of the difference for the two distributions is less than a predefined value (0.05 and 0.01 were used). In this study, we have chosen a subnetwork (a series of reactions with length 5 or 10) to be enriched in one population. The goal is to compare different methods in recovering this significant subnetwork (a set of significant reactions) based on the simulated abundance matrix. Biologically, the enriched pathways indicate functional enrichment of certain biological processes in a microbial community.

The receiver operating characteristic (ROC) curve is plotted for each method (Fig. 3). Fig. 3 shows that MetaPath outperforms all other methods dramatically showing the advantage in finding significant subnetworks. Note that the results tested on our simulated datasets can be considered as the baseline performance, because it contains only one significant subnetwork, whereas real metagenomic datasets typically contain multiple significant pathways. The most commonly used approach — comparing KEGG-defined pathways — performs the worst in our simulation study (Fig. 3).

We used MetaPath to compare the abundances of the metabolic networks of the gut microbiome in lean and obese subjects, relying on data from 3. This metagenomic dataset comprises 6 samples from obese subjects and 6 samples from lean objects. The sequences are annotated and mapped to KEGG reactions using BLASTX (E value < 10^-5, bitscore > 50, and %identity > 50; parameters suggested in the original study), resulting in total 1832 unique reactions within the 12 metagenomic samples. First, we computed p values 16 using Metastats to find differentially abundant reactions. Using a p value cutoff of 0.05, 92.7±9.1 (mean±standard deviation) reactions are significant including 37.1±6.6 and 55.6±3.1 enriched reactions in obese and lean groups, respectively, based on 10 runs of Metastats. The high variance of the number of significant genes can be primarily explained by two reasons: (1) some reactions are slightly below or above significance cutoff (0.05), thus p values computed through bootstrapping will jump between being considered significant and not significant (Fig. 4); (2) there are large variances of the abundance values within individuals in a same phenotypic group. In addition to p values, Metastats also provides an estimate of the False Discovery Rate (q value), information that is not used by MetaPath. The q values for all reactions are 1 (except R01676 where q=0.73), i.e. a literal interpretation of Metastats results would indicate no pathways are significantly different between the two populations. This result can be explained by the flat distribution of the p values (Fig. 4), from which the q values are estimated. This observation highlights the limitation of relying on the false discovery rate, which requires the estimation of the proportion of features that are truly null 16, approach that does not perform well when only few features are truly significant.

We, then, applied MetaPath to this dataset, and have found 9 differentially abundant subnetwork (Fig. 5) using 0.05 cutoff value for both p_abund and p_struct. All these subnetworks are enriched in obese subjects; none was found to be enriched in lean subjects. These 9 significant subnetworks contain 48 unique reactions, 22 of which are significant. It is worth pointing out that the number of significant reactions varies between different runs of statistical permutations (using Metastats) as shown above, but the significant pathways identified by Metapath stay the same (Fig. 5). This observation confirms that the results from MetaPath are more robust in the presence of noise in the data than the gene-by-gene approach. In the p values distribution of subnetworks (Fig. 4), most of them are either very significant or insignificant and very few are around the p value cutoff, allowing the users to easily interpret the results.

Five subnetworks (Fig. 5a-5e) are completely contained in the KEGG Fatty Acid Biosynthesis pathway, which consists of catabolic processes that can generate energy and primary metabolites from fatty acids. Our findings are consistent with previous observations and biochemical analysis in microbiota transplantation experiments in germ-free mice 17, where the concentrations of short-chain fatty acids in the caeca of obese mice are higher than lean mice, suggesting that the gut microbiome in obese subjects has an increased capacity for dietary energy harvest.

Another interesting significant networks consists of 10 reactions (Fig. 5f), of which 8 belong to Cysteine and Methionine Metabolism and 2 belong to Sulfur Metabolism. Many reactions in this subnetwork are connected by the L-Homocysteine molecule. In addition, three other subnetworks (Fig. 5g-5i) we discovered further confirm its potential involvement in obesity, because all these three pathways contain L-homocysteine as metabolite. It is well-known that a high level of blood serum homocysteine is a risk factor for cardiovascular disease 18, and obesity — an increasingly prevalent metabolic disorder — is closely associated with heart disease 19. Significant correlations between plasma homocysteine concentrations and obesity have been previously reported 1820212223. The finding of increased potential for homocysteine metabolism within the obese gut microbiome provides an interesting hypothesis for future studies that, the gut microbiome may either have a direct role in the elevation of homocysteine levels in plasma, or may indirectly affect the hepatic biosynthesis of this amino-acid in the human body.

A second data-set comprises gut microbiome samples from 4 infants and 9 adults individuals which were sequenced by Kurokawa, et al., 2007 7. The sequences were annotated and mapped to the reactions of KEGG pathway using BLASTX (E value < 10^-8, hit length coverage ≥ 50% of a query sequence), resulting in total 1781 unique reactions within the 13 metagenomic samples. Based on 10 runs of Metastats, 383.7±1.56 reactions are significant using p value cutoff of 0.05, including 268.7±1.56 and 115±0 reactions enriched in infant and adult subjects respectively.Using a q value cutoff of 0.05, 167.2±2.7 reactions are significant, including 133.2±2.7 and 34±0 reactions enriched in infant and adult subjects respectively.Compared with the previous dataset (obese and lean twins samples), the predictions of significant reactions are much more consistent across different permutations.

Applying MetaPath to search for significant subnetworks using the same parameters as before, we have found that 6 are enriched in infant subjects (Fig. 6a-6f) and 4 are enriched in adult subjects (Fig. 6g-6j). These 10 significant subnetworks contain 55 unique reactions (35 and 20 in subnetworks enriched in infant and adult, respectively), including 38 significant reactions (22 and 16 enriched in infant and adult, respectively) and 17 reactions not found significant by Metastats. Three subnetworks enriched in infant subjects (Fig. 6a, 6c and 6d) involve the metabolite L-homocysteine, and a fourth one (Fig. 6b) involves L-cysteine – a related amino-acid, which is consistent with previous observation that breastfed babies have an higher plasma homocysteine level possibly caused by suboptimal availability of folate in breast milk 24. The concentration of folate is negatively correlated with that of homocysteine, as folate is a necessary coenzyme for reactions that metabolize homocysteine. In addition, babies normally have high protein diet, which may also cause the concentration of homocysteine to increase. A second pathway in Fig. 6e involves substrates citrate and succinate, and is closely related with oxidative tricarboxylic acid (TCA) cycle. TCA cycle is part of carbohydrate metabolism and can convert carbohydrates into usable energy in aerobic organisms. Because the adult gut ecosystem is dominated by strict anaerobes, it is reasonable to find this subpathway enriched in infant individuals where the gut microbiota also includes aerobes. This finding is consistent with results obtained by comparing COG functional categories 7. We also find a subpathway belonging to atrazine metabolism to be enriched in infant subjects (Fig. 6f). Atrazine is one of the most widely used herbicides, and it contaminates water and soil throughout the world. Our finding possibly indicates a side-effect of this contamination.

The pathway in Fig. 6i (enriched in adult subjects) is part of the lipopolysaccharide biosynthesis. Lipopolysaccharides are a building block of the outer membrane of Gram-negative bacteria. The enrichment of pathway Fig. 6i in adult subject may be a result of the fact that Gram-negative bacteria are also enriched in adults. Specifically, Bacteroides, a genus of Gram-negative bacteria, are a major constituent of adult gut microbiome, but not highly prevalent in infants. Fig. 6h and Fig. 6j (enriched in adult) are pathways related with pyrimidine metabolism. The metabolites RNA, cytidine and uridine, which are contained in pyrimidine metabolism, are normally obtained from high RNA food such as organ meats, broccoli, and brewer’s yeast, which are not available to unweaned infants, as they are not present in high abundance in milk. The pathway in Fig. 6g (enriched in adult) is part of fructose and mannose metabolism a pathway related to carbohydrate metabolism. This is also consistent with COG-based analyses indicating that many mono- or disaccharides metabolism genes are enriched in adults 7, explained by the fact that colonic microbiota in adults uses indigestible polysaccharides as resources for energy production and biosynthesis of cellular components.